An insect of mass m is initially at one end of a stick of length L and mass M, which rests on a smooth floor. The coefficient of friction between the insect and the stick is k. The minimum time in which the insect can reach the other end of the stick is t. Then t2 is equal to

Engineering

Physics

Contact Force

Relative Motion

Newtons Second Law of Motion

Question

An insect of mass m is initially at one end of a stick of length L and mass M, which rests on a smooth floor. The coefficient of friction between the insect and the stick is k. The minimum time in which the insect can reach the other end of the stick is t. Then t² is equal to

2Lm/kgM

2Lm/kg(M+m)

2L/kg

2LM/kg(M + m)

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F_m = mµg ⟹ a_m = µg
F_M = µmg

$a_{M} = \frac{μmg}{M}$

$a_{rel} = a_{M} + a_{m} = μg (1 + \frac{m}{M})$

$L = \frac{1}{2} a_{rel} t^{2}$

$t^{2} = \frac{2 LM}{μg (M + m)}$ .